You're right, this shouldn't be hard to understand. Which just makes you look that much more stupid for not understanding it.
The only qualification for a Darwin award is to remove yourself from the gene pool by death or sterilization. The fact that he had kids already is of no bearing, he was capable of reproducing more, now he can't, he's eligible.
http://www.darwinawards.com/rules/rules1.html
The existence of offspring, though potentially deleterious to the gene pool, does not disqualify a nominee. Children inherit only half of each parent's genetic material and thus have their own chance to survive or snuff themselves. If, for instance, the offspring has inherited the "Play With Combustibles" gene, but also has inherited the "Use Caution When..." gene, then she is a potential innovator and asset to the human race. Therefore, each nominee is judged based on whether or not she has removed her own genes, without consideration to the number of offspring or, in the case of an elderly winner, the likelihood of producing more offspring.